Question: An LTI discrete-time system has frequency response given by (a) Use of the above form of the frequency response to obtain an equation for the

An LTI discrete-time system has frequency response given by

H(ej) = (1 je~jw)(1+jejw) 1-0.8e-ja = 1+e-j200 1-0.8e-jo 1 1-0.8e-jo + e-j200

(a) Use of the above form of the frequency response to obtain an equation for the impulse response h[n] of the system.

(b) From the frequency response, determine the difference equation that is satisfied by the input x[n] and the output y[n] of the system.

For what value of ? _o will the output be of the form

For - ?

H(ej) = (1 je~jw)(1+jejw) 1-0.8e-ja = 1+e-j200 1-0.8e-jo 1 1-0.8e-jo + e-j200 1-0.8e-jo x[n] = 4 + 2 cos(won) for- y[n] = A= constant

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